1. Field of the Invention
This invention relates generally to an apparatus and method for sampling rate conversion. More particularly, this invention relates to an apparatus and method for sampling rate conversion by the use of DFT and IDFT techniques which utilize the Chirp-Z transform method including a fast Fourier transform (FFT) for convolution computations whereby the complexity of the conversion is reduced to an order of O(N log N).
2. Description of the Prior Art
As there is an ever increasing need for applying the sampling rate conversion to various digital signal processing systems, such as the vocoders, digital waveform coding systems, digital audio systems, and various modulation systems, the technology of the sampling rate conversion is still limited by two major technical limitations. The first limitation is due to the fact that the traditional techniques for sampling rate conversion are limited to rate changes with factors which are decimated by integers or interpolation by integer factors. These techniques cannot be applied to some digital signal processing systems such as the pitch shifter of a high definition music synthesizer and various digital audio systems which may require 44.1K/48K or 32K/44.1K conversions. Second limitation arises when the sampling rate conversion algorithms based on a Shannon-Whittaker's interpolation formula is applied. The algorithms were proposed in attempt to overcome the first limitation. Due to the highly computational complexity, i.e., O(N.sup.2) and large database requirements, the proposed technique based on the Shannon-Whittaker's interpolation scheme is not suitable for real time applications and becomes impractical for implementation in modern systems which have urgent need for high speed, less complex apparatus and algorithms to perform the tasks of sampling rate conversion.
Traditional methods of sampling rate conversion generally requires the employment of interpolation to perform a conversion with a rational conversion factor of L/M where L and M are two integers. One of the common methods used consists the steps of inserting (L-1) zeros as the sampled values. The signals with the inserted zeros are processed with a up-sampled rate filter and decimated by rejecting all but every M-th sample. This method is not suitable for some digital audio systems. In the case of shifting the pitch in a music synthesis system, the A4 tone has the basic frequency of 440 Hz and A5 at 880 Hz. There are twelve semi-tones between A4 and A5. The frequency of each of these semi-tones can be obtained by the use of following formula: EQU f.sub.i =440*2.sup.(i/12) ( 1)
In accordance with the Equation (1), when shifting a sampled signals representing an A4 tone to a A4-sharp, i.e., A#4, wherein i=1 in Equation (1), there is no rational number to represent the conversion factor of 2.sup.(1/12) and the traditional rate conversion method is not suitable to perform the task required in such application.
For the purpose of illustrating the state of the art and to demonstrate the fact that there is a strong need for novel and improved sample rate conversion techniques to overcome these limitations, examples of two issued patents are reviewed herein. Yamada et al. disclose in U.S. Pat. No. 4,870,661 entitled "Sample Rate Conversion System, Having Interpolation Function" (Issued on Sep. 26, 1989), a sample rate conversion means for converting the sampled data at a first sampling rate to the data suitable to be used for a second system with a different sampling rate. The sample rate conversion means has an interpolation means to compute the interpolation coefficients which are then used by the interpolation means to to perform the interpolation task for converting the sampling rate. The interpolation coefficients are computed based on the phase relationship between the clock signals of the first and the second clock signals.
The sampling rate conversion means disclosed by Yamada et al. is particularly useful for processing video signals to be received and displayed on the television screen. The usefulness of this rate conversion means which uses an interpolation technique as disclosed in this patent however is not able to overcome the limitation that the conversion can only be performed based on a conversion ratio of a rational number. The interpolation means which computes the interpolation coefficients based on the phase relationship using the first and the second frequencies of the two system docks. The interpolation coefficient is then computed as the ratio of the time interval between the sampled data of the first frequency and the dock signal of the second system and the time interval between the next sampled data point with the next system clock of the second system. The interpolation coefficient is then used as a multiplier which is then provided to a filter to perform the rate conversion. For various modern applications, specifically, in the audio synthesis systems for pitch shifting, this interpolation is not suitable.
Takayama et al. discloses in another U.S. Pat. No. 5,068,716 entitled `Sampling Rate Converter` (issued on Nov. 26, 1991) a sampling rate converter which is employed to convert an input video signal having an input sampling frequency to a second and different sampling frequency. An over-sampled technique is used wherein the input signals are over-sampled at a frequency which is an integral multiple of the input sampling frequency so as to generate zero values between data of the input signals. An interpolation is then performed on the over-sampled output signals. The interpolated signals are then decimated to generate the video signals with the desired second sampling rate. The video signals with the second sampling frequency is then filtered by a low pass filter to remove erroneous data caused by the sampling rate conversion.
Even that the sampling converter as disclosed by Takayama et al. provides a converter which is relatively simpler in its circuit architecture and still capable of providing adequate accuracy for the purpose of video signal processing, however, like the converter disclosed by Yamada et al., this patent is restricted by the same limitation. The conversion can only be performed for a rational factor. Additionally, the multi-stages of circuits which are required for performing the tasks of interpolation, decimation and filtering impose a great demand on the IC chip areas thus may often limit the application of this rate conversion devices to larger and more expensive systems. Broad application of a low cost and miniaturized sampling rate converter suitable for more common use by the consumer electronics products and the portable communication systems would therefore be greatly restricted.
The aforementioned difficulties and limitations are further compounded by the fact that a device designer of the conventional sampling rate conversion apparatus is provided with little flexibility due to the limitation imposed by the interpolation operations. The circuit architecture and functions performed therein are well defined. With the system speed requirements, the designer often is required to apply a multi-stage structure as that disclosed in the techniques disclosed by Takayama and Yamada. This lack of design flexibility further restricts the sampling conversion devices from being optimized for different types of applications with broader range of design complexity, manufacture costs, size and performance levels.
Therefore, there is still a need in the art of sampling rate conversion to provide an apparatus and algorithm such that the conversion process can be flexibly performed for frequency shifting wherein the rates of conversion are not rational numbers. Furthermore, the task of conversion must be expeditiously performed with high speed in order to satisfy the real time data processing requirements. Meanwhile, in order to apply the IC technology to fabricate the conversion devices, the circuit configuration of the converter for implementing the algorithm must be simple, small in size and easy to design and manufacture such that the conversion devices can be broadly and economically applied to a wide variety of modern electronics and communication systems.